RG flows in d dimensions, the dilaton effective action, and the a-theorem

Abstract

Motivated by the recent dilaton-based proof of the 4d a-theorem, we study the dilaton effective action for RG flows in d dimensions. When d is even, the action consists of a Wess-Zumino (WZ) term, whose Weyl-variation encodes the trace-anomaly, plus all Weyl-invariants. For d odd, the action consists of Weyl-invariants only. We present explicit results for the flat-space limit of the dilaton effective action in d-dimensions up to and including 8-derivative terms. GJMS-operators from conformal geometry motivate a form of the action that unifies the Weyl-invariants and anomaly-terms into a compact general-d structure. A new feature in 8d is the presence of an 8-derivative Weyl-invariant that pollutes the O(p^8)-contribution from the WZ action to the dilaton scattering amplitudes; this may challenge a dilaton-based proof of an a-theorem in 8d. We use the example of a free massive scalar for two purposes: 1) it allows us to confirm the structure of the d-dimensional dilaton effective action explicitly; we carry out this check for d=3,4,5,...,10; and 2) in 8d we demonstrate how the flow (a_UV - a_IR) can be extracted systematically from the O(p^8)-amplitudes despite the contamination from the 8-derivative Weyl-invariant. This computation gives a value for the a-anomaly of the 8d free conformal scalar that is shown to match the value obtained from zeta-function regularization of the log-term in the free energy.

31 pages, 7 figures. v.2 minor corrections, references added

References in corpus (11)

• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• On renormalization group flows and the a-theorem in 6d
• Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
• The Conformal Anomaly of M5-Branes
• Entanglement entropy for even spheres
• Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?
• Entanglement entropy for odd spheres
• On c-theorems in arbitrary dimensions

Cited by in corpus (41)

• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• Constraints on RG Flow for Four Dimensional Quantum Field Theories
• Renormalization Group Flows on Line Defects
• Recursion relations from soft theorems
• New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order
• Scattering Amplitudes from Soft Theorems and Infrared Behavior
• Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT
• Exploring soft constraints on effective actions
• Structures on the Conformal Manifold in Six Dimensional Theories
• Defect $a$-Theorem and $a$-Maximization
• Double-soft behavior of the dilaton of spontaneously broken conformal invariance
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Higher Derivative Terms, Toroidal Compactification, and Weyl Anomalies in Six-Dimensional (2,0) Theories
• The a-function for gauge theories
• The spectrum of IIB supergravity on AdS_5 x S^5/Z_3 and a 1/N^2 test of AdS/CFT
• Scale invariance vs conformal invariance
• Soft theorems from anomalous symmetries
• Perturbative c-theorem in d-dimensions
• Mutual information and the F-theorem
• The a-theorem and entanglement entropy
• The a-function in six dimensions
• Spontaneous Symmetry Breaking, Conformal Anomaly and Incompressible Fluid Turbulence
• All the entropies on the light-cone
• The a-function in three dimensions: beyond leading order
• An Effective Theory for Holographic RG Flows
• Scheme invariants in phi^4 theory in four dimensions
• A Holographic Study of the $a$-theorem and RG Flow in General Quadratic Curvature Gravity
• The a-function for N=2 supersymmetric gauge theories in three dimensions
• The dilaton Wess-Zumino action in higher dimensions
• Dilaton Effective Action with $\mathcal{N}=1$ Supersymmetry
• The chirality-flow formalism for the standard model
• Renormalization Group Flows, the $a$-Theorem and Conformal Bootstrap
• Defect Localized Entropy: Renormalization Group and Holography
• Dilaton invading from infinitesimal extra dimension
• Equivalence of EFTs and Time-Like Extra Dimensions
• Gradient flows in three dimensions
• The a-theorem for the four-dimensional gauged vector model
• Unitarity methods for scattering in two dimensions
• A Light Dilatonic Higgs and a Dilatonic Inflaton in the Georgi-Glashow SU(5) Model
• Quantum Field Theory on spherical space forms
• The a-theorem for the four-dimensional vector model